It is standard practice to deform a sheet of glass while it is still very hot and somewhat plastic from a substantially two-dimensional planar shape into a more complex three-dimensional shape. However, in order to have a finished product of acceptable quality and without defects that would cause the finished product to be weakened and form optical distortions, multiple post shaping operations, such as grinding to maintain uniform thickness, must be performed. Glass structures with a non-uniform thickness are associated with undesirable characteristics including optical distortions and reduced structural rigidity. While performing a post-shaping operation such as grinding can reduce the uneven thickness prevalent in conventionally formed curved glass structures, such post-shaping techniques are costly, time-consuming, and cannot sufficiently control the variation in thickness of the shaped glass substrate.